Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups

Alan W. Reid; Shicheng Wang; Qing Zhou

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arXiv · math/0002003

Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups

Alan W. Reid·Shicheng Wang·Qing Zhou

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Abstract

We address a conjecture that $π_1$-surjective maps between closed aspherical 3-manifolds having the same rank on $π_1$ must be of non-zero degree. The conjecture is proved for Seifert manifolds, which is used in constructing the first known example of minimum Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3-manifolds.

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BibTeX RIS

Alan W. Reid, Shicheng Wang, Qing Zhou. 2000-02-01. Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups. https://arxiv.org/abs/math/0002003

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